With a concave mirror, an object is placed at a distance `x_(1)` from the princiipal focus, on the principal axis. The image is formed at a distance `x_(2)` from the principal focus. The focal length of the mirror is

Options

A. `x_(1)x_(2)`
B. `(x_(1)+x_(2))/2`
C. `sqrt((x_(1))/(x_(2)))`
D. `sqrt(x_(1)x_(2))`

Explanation

(d) As `1/u+1/v=1/f`
`:.1/((f-x_(1))+1/((x_(2))))=1/f`
`implies (f-x_(2)+f-x_(1))/((f-x_(1))(f-x_(2)))=1/f`
`impliesf^(2)-fx_(2)-fx_(1)+x_(1)x_(2)=2f^(2)-f(x_(1)+x_(2))`
`implies f^(2)=x_(1)x_(2)impliesf=sqrt(x_(1)x_(2))`